Circuit for defining the dye dilution curves in vivo and in vitro for calculating the cardiac blood flowrate value per minute

ABSTRACT

The invention concerns a circuit for the determination of the concentration of any component of a liquid containing three different components having different optical properties, for the determination of the concentration sum of all components and of one other component, for the determination of the product and of the quotient which is formed by the third component, and for the calculation of the blood volume per minute of the heart. One or more light sources, a light sensing element, an optical filter and a lens are disposed in the circuit, and also power supply circuits and control circuits. To these are added a signal converting unit or a sensing system operating on three wavelengths other than the isobestic points or on a range containing these points, containing optical measurement channels, and measuring on the transmission or reflection principle. 
     The signals delivered by the three-channel sensor or by the signal converter, as the case may be, are processed by logarithmatic circuits. The logarithmating circuits are connected to channel amplifiers, and to the latter are connected subtraction circuits and multiplication circuits. 
     By means of the electronics of suitable construction it is possible to determine in vivo and in vitro both the change with time of the concentration of the dye placed in the blood at any point in the circulatory system, and the volume of the blood.

In its broadest aspect, the apparatus according to the invention issuitable for determining the liquid concentration of three components ina liquid containing three components with different optical propertiesand is suitable for determining the quotient of any two components orthe quotient of the sum of two components and of the third component. Bymeans of the apparatus it is also possible to determine the quotient ofa product of two components and of the third component. The use of theapparatus is significant in medical laboratories. In first place, it isused for determining the cardiac output and this use will be the subjectof the description.

However, the invention relates particularly to a circuit for definingthe dye dilution curves in vivo and in vitro for calculating the cardiacoutput.

With apparatus according to the invention it is possible to measure thechange with respect to time of the concentration of the dye introducedat a random place of the circulation - the dye dilution curve - thevolume of the blood in the circulation and the oxygen saturation of theblood in vivo (by a photometric transducer applied to the surface of thebody) and in vitro by means of a photometric catheter transducerintroduced into the circulation or by means of a photometric measurementperformed on the blood sample. With these means it is also possible todetermine in vivo the pulse curve whose amplitude is independent of thechange of oxygen saturation of the blood or it is possible to define invitro the total content of haemoglobin in the blood per minute.

The quantity of blood pumped through the left ventricle of the heartinto the blood circulation is an important characteristic of cardiacperformance. This quantity of blood is referred to as "volume perminute". In the course of time, several methods, referred to in theirentirety as indication-dilution methods, were developed for determiningthis quantity of blood. The common feature of these methods is that thedependence on time of the physical characteristics (activity,concentration, temperature) is determined at a selected place of thearterial system by the indicator material (radioactive isotope, dye,cold or warm NaCl solution) which is introduced into the blood, theindicator material being introduced via a vein. The cardiac output canbe defined by known methods from the so-called indicator-dilution curvethus obtained.

Because of its advantageous features, the dye dilution system is used inmost cases. The apparatus according to the invention comprises a circuitsuitable for such a process. Earlier processes and apparatus suffer fromseveral disadvantages. The fundamental causes of these are to be foundin the special properties of the object that is to be measured. Bloodcan be regarded as a liquid containing three components, at least fromthe point of view of dye dilution examination. These components are: theoxidized haemoglobin (O₂ Hb), the reduced haemoglobin (red.Hb) and thedye. The first two can assume values which vary physiologically withrespect to time, thus making it difficult to determine theconcentration-time dependence of the dye. This problem can be explainedclearly by reference to FIG. 1 which shows the change with respect totime of the absorption coefficients (in dependence on the wavelength) ofthe curve expressing O₂ Hb (curve 1), the curve expressing red.Hb (curve2), the curve expressing a blue dye (Evans blue, curve 3) and the curveexpressing a green dye (cardio green, curve 4).

The use of the blue dye is restricted because the absorptioncoefficients of O₂ Hb and red.Hb differ widely at the wavelength oftheir maximum absorption. The accuracy of determining the timedependence of the dye concentration is therefore greatly influenced bythe change of oxygen saturation which occurs in the course ofmeasurement. The dye dilution curve thus obtained is therefore used onlyfor qualitative measurements and not for calculating the cardiac output.The difference between the absorption coefficients of O₂ Hb and red.Hbat their maximum absorption wavelength of green dyes is not very great,in other words in an ideal case the measurement of the discretewavelength (805 nm) at the isosbestic point is zero. However, thebandwidth of the measuring channel in such apparatus can in practice bereduced at most down to 10-15 nm. The interference effect of oxygensaturation must therefore be taken into account. This interferenceeffect can be reduced by appropriate selection of the quantity ofinjected dye of a specific value. A dye of this kind is therefore usedfor the dilution curve to calculate the cardiac output. In view of thefact that the injected quantity of dye is limited by methodic andphysiological factors, it follows that the accuracy achieved in such acase is also only limited. A further disadvantage of apparatus knownhitherto is due to the fact that the end concentration of the dye in theblood sample must be determined before and after the measurement in thecase of in vivo measurements. (This value is designated by C_(3V) in thedye dilution curve). The examination thus becomes complex, the errorsources increase (two samples must be taken and the samples must beprepared and measured) and a second apparatus should therefore be used.

A further disadvantage of the apparatus known hitherto is that in thecase of in vivo measurements the measuring accuracy is impaired, moreparticularly any further mechanized processing of the dye dilutioncurve, namely due to the pulse curve which is superimposed on the usefulindication. Solutions which are acceptable to a greater or lesser degreeand promise a reliable result are adopted to avoid this defect and leadto success only if different conditions are given. However, thisinterference effect in every case gives rise to a problem.

By means of the apparatus according to the invention it is possible todetermine the dye dilution curve and the correct value of the endconcentration to calculate the cardiac output, apart from permitting theuse of any desired dye; changes of oxygen saturation or of the pulsecurve which take place in the course of in vivo and in vitromeasurements can be eliminated so that the measurement is not subject toany interference.

With the apparatus it is also possible to determine, in the case of invivo measurements, the pulse curve whose amplitude is independent of achange of oxygen saturation and, on the basis of a knowledge of thetotal haemoglobin content of the patient's blood, it is possible todetermine the blood volume in the circulation and in the case of invitro measurements it is possible to determine the oxygen saturation ofthe blood, the total haemoglobin content and the volume of the blood inthe circulation. The apparatus according to the invention is alsosuitable for observing elimination through the liver in vivo of the dyeintroduced into the blood circulation, that is to say for investigatingso-called liver functions.

To convert the signals the apparatus according to the invention containsthree light sources which operate simultaneously on a wavelength whichdeviates from the isosbestic point or points or include the said pointor points. The apparatus also contains a light sensing element a sensoror sensor transducer unit incorporating an optical filter and lens,adapted to measure on the transmission principle or reflection measuringprinciple and having an optical measuring channel. It also containscircuits for feeding and controlling the said unit. Advantageously, thesignals are converted by circuits which co-operate with the samelight-sensitive element in time multiplex operation, contain one or moresolid-state light sources, an optical filter and a lens, as well ascontrol and power circuits and are adapted for storing and filtering thesampled signal, the said circuits incorporating sensor or signaltransducer units. The electrical signals which are supplied through thethree-channel sensors or through the signal transducer are processed bycircuits with logarithmic functions. The outputs of these circuits areconnected to channel amplifiers for adjusting the characteristicfeatures which are identical for optical reasons. The logarithmic effectcan be achieved by providing a light sensor comprising one or morephotovoltaic cells which are advantageously terminated by a workingresistor which is larger by 50 kohms. A voltage which is proportionalwith a good approximation to the logarithm of the intensity of the lightthat strikes the photovoltaic cells will in this case appear at theterminals of the said light sensing element.

The general circuit arrangement comprises the subtracting circuits thatfollow the channel amplifiers, the subtracting circuits and thosecontaining the scale, scale adjusting circuits and multiplying circuitsor an electrical network comprising a combination of the above and onwhose outputs appear the electrical signals which are proportional tothe concentration values or to the sums thereof. The individual circuitsare constructed as follows in accordance with their function:

As already mentioned, the apparatus comprises one or more light sources,light sensing elements, optical filters and lenses as well as threesensor elements or signal transducing units adapted to measure by thetransmission or reflection principle and containing optical measuringchannels and adapted to operate in the wavelength range which deviatesfrom the isosbestic points or includes them, as well as logarithmicfunction generators L1, L2, L3 connected thereto and channel amplifierswhich are connected to the latter circuits. Of the said channelamplifiers, the output of the first channel amplifier A1 is directlyconnected to one input of a first subtracting circuit H1, the output ofthe second channel amplifier A2 is directly connected to one input of asecond subtracting circuit H2, and the output of the third channelamplifier A3 is directly connected to one input of a third subtractingcircuit H3. The output of the first channel amplifier A1 is connectedthrough a branch and via a multiplier circuit M1 to the other one inputof the third subtracting circuit H3, the output of the second channelamplifier A2 is connected through a second multiplier circuit M2 to theother input of the first subtracting circuit H1, the output of the thirdchannel amplifier A3 is connected through a further multiplier circuitM3 to the other input of the second subtracting circuit H2. Of thesubtracting circuits H1, H2, H3 which are directly connected to thechannel amplifiers A1, A2 and A3, the output of the first subtractingcircuit H1 is directly connected to one input of a fourth subtractingcircuit H4, the output of the second subtracting circuit H2 is directlyconnected to one input of a first subtracting and scale adjustingcircuit U1, the output of the third subtracting circuit H3 is directlyconnected to one input of the second subtracting and scale adjustingcircuit U2. The output of the first subtracting circuit H1 is connectedthrough a fourth multiplying circuit M4 to the other input of the secondsubtracting and scale adjusting circuit U2, the output of the thirdsubtracting circuit H3 is connected to the other input of the fourthsubtracting circuit H4 through a fifth multiplier circuit M5. The outputof the fourth subtracting circuit H4 is connected on the one handdirectly to the input of a scale setting circuit G1 and on the otherhand, through a sixth multiplier circuit M6, to the other input of thefirst subtracting and scale setting circuit U1. The output of the scalesetting circuit G1 is connected to one input of a summing network Σ andto the display unit DP. The output of the first subtracting and scalesetting circuit U1 is connected to a first input of a quotient-formingand multiplying circuit MD and to the display unit DP, the output of thesecond subtracting and scale setting circuit U2 being connected on theone hand to the second input of the summing network Σ and on the otherhand to the display unit DP and to a first input of the circuit D whichforms the quotient. The output of the summing network Σ is connected onthe one hand to the quotient-forming and multiplying circuit and on theother hand to the second input of the quotient-forming circuit D and tothe display unit DP. An adjustable potentiometer P4 for precisioncontrol is connected to the third input of the quotient-forming andmultiplying circuit MD. The output of the quotient-forming andmultiplying circuit MD is connected to the display unit DP and to thethird input of the quotient-forming circuit D. A second adjustablepotentiometer P5 for precision control is connected to the fourth inputof the quotient-forming circuit D, the three remaining outputs of thequotient-forming circuit being connected to the display unit DP (seeFIG. 3).

The apparatus according to the invention can also be constructed so thatthe output of the first channel amplifier A1 is directly connected to asubtracting circuit H5 which is first in series, the output of thesecond channel amplifier A2 is directly connected to a first input of asecond subtracting circuit H6, and the output of the third channelamplifier A3 is directly connected to one input of a third subtractingcircuit H7. The output of the first channel amplifier A1 is connectedvia a multiplying circuit M7 to the second input of the secondsubtracting circuit H6, the output of the second channel amplifier A2 isconnected through a first multiplier circuit M8 to the other input ofthe third subtracting circuit H7 and through a second multiplyingcircuit M9 to the second input of the subtracting circuit H5 which isthe first in series. The output of the subtracting circuit H5, which isthe first in series, is directly connected to a first input of a fourthsubtracting circuit H8, the output of the second subtracting circuit H6is directly connected to a first input of a subtracting and scalesetting circuit U3, and the output of the third subtracting circuit H7is directly connected to a first input of the second subtracting andscale setting circuit U4, the output of the first subtracting circuit H5being connected through a multiplier circuit M10 to the second input ofthe second subtracting and scale setting circuit U4, the output of thethird subtracting circuit H7 being connected through a furthermultiplying circuit M11 to the second input of a further subtractingcircuit H8 which is the fourth in series. The output of the fourthsubtracting circuit H8 is directly connected on the one hand to theinput of a scale setting circuit G2 and on the other hand, through afurther multiplying circuit M12, to the other input of the firstsubtracting and scale setting circuit U3 which is the first in series.The output of the scale setting circuit G2 is connected to the displayunit DP and to one input of a summing network Σ. The output of the firstsubtracting and scale setting circuit U3 is connected to the displayunit DP and to one input of a quotient-forming and multiplying circuitMD. The output of the second subtracting and scale setting circuit U4 isconnected to the second input of the above-mentioned quotient-formingand multiplying circuit MD and is also connected to the second input ofthe summing network Σ as well as to the display unit DP but the outputof the summing network Σ is connected on the one hand to the displayunit DP and on the other hand to the third input of the quotient-formingand multiplying circuit MD (which contains a total of six inputs).Adjustable precision potentiometers P4, P5, P6 are connected to thefourth, fifth and sixth inputs of the quotient-forming and multiplyingcircuit MD, the outputs thereof being connected to the display unit. Themultiplying circuit performs a multiplication the factors of which areformed by the electrical signals which reach the input of the saidcircuit and by the linear combination of the absorption coefficients ofthe component that is to be measured and by a constant number. In thecase of multiplication with a number which is smaller than unity, thesaid multiplying circuit is embodied as a potentiometer and/or a voltagedivider comprising fixed resistors. It can also be constructed as anemitter follower or an amplifier stage comprising a potentiometer and/orfixed resistors and being connected downstream of the voltage divider;if multiplication is performed with a number which is greater than unitythe said module is constructed as an amplifier stage. The subtractingcircuit performs the subtraction of two electric signals which aresupplied to its input. The circuit is embodied as a subtractingoperational amplifier or a summing operational amplifier. Thesubtracting and scale setting circuit performs the subtraction of oneelectric signal from the other, both of which are applied to the inputsof the said circuit. The circuit can be constructed as a subtractingoperational amplifier or as a summing operational amplifier. Thesubtracting and scale setting circuit subtracts one electric signal fromthe other supplied to its inputs. The correct scale of an electricsignal which is proportional to the given concentration is set up byappropriate selection of the amplification factor. This embodiment ofthe said module corresponds to the subtracting circuit.

The scale of the electric signal which is proportional to the givenconcentration is set up by appropriate selection of the amplificationfactor of this circuit. This circuit is embodied as an operationalamplifier.

The summing network adds the electric signals applied to its inputs.This circuit is embodied as a adding operational amplifier or asubtracting operational amplifier.

Further processing of the electric signals which are proportional to theindividual concentrations or sums of the said concentrations isperformed in the quotient-forming circuit which divides two electricsignals that are variable with respect to time or is performed in thequotient-forming and multiplying circuit which divides two signals whichvary with respect to time or by multiplication of the result thereofwith an electric signal which is variable with respect to time or notvariable with respect to time (having unity value).

Depending on the particular embodiment, the apparatus comprises settingpotentiometers which provide signals or apply precision control for theamount of injected dye, for the total haemoglobin content of the patientor the final concentration of the dye. Indicating instruments toindicate the measured values are also provided.

The invention will now be explained hereinbelow by reference to diagramsor drawings which illustrate the individual embodiments and in which:

FIG. 1 is a graph showing the change with respect to time of theextinction factors of O₂ Hb and red.Hb and the dyes of Evans blue andcardio green, plotted against the wavelength λ.

FIG. 2 is a characteristic dye dilution curve (the concentration valuesare plotted on the ordinate and the time is plotted on the abscissa).

FIG. 3 shows a circuit of one embodiment of the invention.

FIG. 4 shows the circuit of another embodiment of the invention.

FIGS. 5-10 show further embodiments.

FIGs. 11-14 show circuits of the embodiments illustrated in FIGS. 3-10.

FIGs. 15-28 show further embodiments of the invention according to FIGS.3 and 4, and

FIGS. 29-31 show further embodiments of the invention according to FIGS.15-28.

All the drawings show the circuits in diagrammatic form.

The features of the apparatus will be related to the case of the mostfrequently employed cardio green dye and to the transducer which isplaced upon the surface of the body for measuring in vivo and adapted tooperate by the transmission principle. Measurement performed by thetransmission principle can be mathematically exact, measurementperformed by the reflection principle on the other hand is subject toseveral limitations and can merely be regarded as an approximate method.

In describing the relationship a simplification is introduced which doesnot however influence the nature of the invention but according to whichthe individual concentration values as well as the dependence on time ofthe measured thickness of the sample as well as the measurement itselfis performed at a discrete wavelength.

The wavelengths of the individual measuring channels (see FIG. 1) aregiven in the following sequence:

λ₁ = 650 nm

λ₂ = 820 nm

λ₃ = 900 nm.

The following terms will be used:

C₁ o₂ hb concentration

C₂ red.Hb concentration

C = c₁ + c₂ total haemoglobin content concentration

C₃ dye concentration

Σ₁, Σ₂, Σ₃ absorption coefficients of O₂ Hb, of red.Hb and the dye atwavelength λ₁.

α₁, α₂, α₃ O₂ Hb, red.Hb and dye absorption coefficients at wavelengthλ₂.

β₁, β₂, β₃ O₂ Hb, red.Hb and dye absorption coefficients at wavelengthλ₃ (see FIG. 1).

φ₀₁, φ₀₂, φ₀₃ intensity of the light incident in the sample undermeasurement on wavelengths λ₁, λ₂ and λ₃.

φ₁, φ₂, φ₃ Intensity of the light transmitted through the sample atwavelengths λ₁, λ₂ and λ₃.

d Thickness of the measured sample.

The relationships are described by reference to FIG. 3. The electricalsignals supplied by the transducer T are connected to the input of thelogarithmic function generators L1, L2 and L3. (The transducer Tcontains one or more light sources, fed by the feed circuit TM, anoptical filter, a light sensing element and three optical measuringchannels for retaining and filtering the obtained signal in the event ofoperation based on the time-multiplex principle).

The signals which are connected to the inputs of the logarithmicfunction generators are characterized on the basis of the Lambert-Beerlaw as follows:

    - ε.sub.1 C.sub.1 d - ε.sub.2 C.sub.2 d - ε.sub.3 C.sub.3 d φ = φ.sub.o1.sup.10                     1.

    - α.sub.1 C.sub.1 d - α.sub.2 C.sub.2 d - α.sub.3 C.sub.3 d φ = φ.sub.o2.sup.10                             2.

    - β.sub.1 C.sub.1 d - β.sub.2 C.sub.2 d - β.sub.3 C.sub.3 d φ = φ.sub.o3.sup.10                               3.

After the logarithmic operation performed in the logarithmic functiongenerators the above expressions assume the following form:

    log φ.sub.1 = log φ.sub.o1 - ε.sub.1 C.sub.1 d - ε.sub.2 C.sub.2 d - ε.sub.3 C.sub.3 d     4.

    log φ.sub.2 = log φ.sub.o2 - α.sub.1 C.sub.1 d - α.sub.2 C.sub.2 d - α.sub.3 C.sub.3 d         5.

    log φ.sub.3 = log φ.sub.13 - β.sub.1 C.sub.1 d - β.sub.2 C.sub.2 d - β.sub.3 C.sub.3 d                        6.

The electrical signals corresponding to the equation are supplied to theinputs of the channel amplifiers A1, A2, A3 which are adjusted foridentical optical characteristics. Electrical signals of identicalmagnitude appear at the outputs of the channel amplifiers A1, A2 and A3if the measured sample has identical optical properties in the threewavelength ranges. The outputs of the channel amplifiers A1, A2, A3 areset to zero when the sample to be compensated by the potentiometers P1,P2 and P3 is placed in the sensor. After performing the function, thefollowing relationships are obtained: ##EQU1##

The equations 7, 8 and 9 are multiplied by the multiplier circuits M1,M2 and M3 with the constants β₃ /ε₃, ε₃ /α₃ and α₁ /β₁ : ##EQU2##

Equation 7 is subtracted from the equation by means of the subtractingcircuit H1; ##EQU3##

The following terms can be introduced: ##EQU4##

After introducing these terms, equation 13 can be written as follows:

    Z.sub.1 = K.sub.1 C.sub.1 d + K.sub.2 C.sub.2 d            17.

Only two unknown concentration values will be found on the right handside of the equation, i.e. in the output signal of the subtractingcircuit H₁.

Equation 8 is subtracted from equation 12 by means of the subtractingcircuit H2 as follows: ##EQU5##

The following terms can then be introduced: ##EQU6##

Equation 18 therefore assumes the following form:

    Z.sub.2 = K.sub.3 C.sub.2 d + K.sub.4 C.sub.3 d            22.

Only two unknown concentration values will be found on the right-handside of the equation, i.e. in the output signal of the subtractioncircuit H2.

Equation 9 is subtracted from Equation 10 by means of the subtractingcircuit H3 as follows: ##EQU7##

The following terms can then be introduced: ##EQU8##

After introducing the above-mentioned terms, Equation 23 assumes thefollowing form:

    Z.sub.3 = K.sub.5 C.sub.1 d + K.sub.6 C.sub.2 d            27.

Only two unknown concentration values will be found on the right-handside of the equation or in the output signal of the subtraction circuitH3.

Equation 27 which expresses the output signal of the subtraction circuitH3 must be multiplied with a constant K₁ /K₅ by means of the multipliercircuit M5, and Equation 17, which merely expresses the output signal ofthe subtraction circuit H1, must be subtracted by means of thesubtraction circuit H4. The output signal of the subtraction circuit canthen be expressed as follows:

    (K.sub.1 /K.sub.5) Z.sub.3 - Z.sub.1) = (K.sub.1 /K.sub.5) K.sub.6 - K.sub.2) C.sub.2 d                                        28.

It is a condition for correct operation that the gain of the subtractioncircuits H1, H2, H3 and H4 shall be equal (this has not been indicatedin the written equations). The scale of the selected signal is set up bythe scale setting circuit G1 which is connected to the output of thesubtraction circuit H4. Due to the presence of a factor σ₂ the outputsignal of the scale setting circuit G1 can be expressed by the followingequation:

    σ.sub.2 (K.sub.1 /K.sub.5) Z.sub.3 - Z.sub.1) = σ.sub.2 (K.sub.1 /K.sub.5) K.sub.6 - K.sub.2) C.sub.2 d           29.

If the left-hand side of the equation is replaced by Y and the constantfactor of the C₂ is replaced by the constant K, the equation will takethe following form:

    Y = KC.sub.2 d                                             30.

Equation 17, which merely expresses the output signal of the subtractioncircuit H1, must be multiplied with a constant value of K₆ /K₂ by meansof the multiplier circuit M4 and the Equation 27, which merely expressesthe output signal of the subtracting circuit H3, must be subtracted bymeans of the subtracting and scale setting circuit U2. The equation canthen be written as follows with respect to the factor σ₁ which sets thescale: ##EQU9##

If the left-hand side of the equation is substituted by X and theconstant factor of C₁ is replaced by a constant K, the equation can thenbe written as:

    X = K C.sub.1 d                                            32.

Equation 28, which expresses the output signal of the subtractioncircuit H4, is thus multiplied by means of the multiplier circuit M6with a constant K₃ /(K₆ (K₁ /K₅) - K₂) and is subtracted from Equation22 (which represents the output signal of the subtracting circuit H2) bymeans of the subtraction and scale setting circuit U1. In view of thescale setting factor σ₃, the equation then takes the following form:##EQU10##

If the left-hand side of the equation is replaced by W and the constantfactor of C₃ is replaced by K, the equation will take the followingform:

    W = K C.sub.3 d                                            34.

To summarize, it may be noted that an electrical signal of the samescale and proportional to C₂ appears on the output of the scale settingcircuit G1, a like signal proportional to C₁ appears at the output ofthe subtracting and scale setting circuit U2 and a like signalproportional to C₃ appears at the output of the subtracting and scalesetting circuit U1. The output signals of the scale setting circuit G1and of the subtracting and scale setting circuit U2 are summated by thesumming network Σ as follows:

    X + Y = K (C.sub.1 + C.sub.2) d = K C d                    35.

Due to the dependence of the value d on time, in the case of in vivomeasurements, a pulse curve whose amplitude is independent on the changeof oxygen saturation will appear at the output of the summing network Σ.The output signal of the summing network Σ as well as the signal of thesubtracting and scale setting circuit U2 are transferred to thequotient-forming circuit D which forms a signal proportional to theoxygen saturation S by forming the quotient from both signals:

    S = (X/X + Y) = (K C.sub.1 d/K(C.sub.1 + C.sub.2) d) = (C.sub.1 /C) 36.

this expression no longer includes d, the value of S is therefore nolonger changed by any alteration with respect to time of the thicknessin the measured sample.

The signal which is proportional to the concentration C₃ and isindependent on the thickness d of the sample is determined by thequotient-forming and multiplier circuit MD from the output signal of thesumming network Σ as well as from the output signal of the subtractingand scale setting circuit U1 and from an electrical signal K'C which isproportional to the total haemoglobin content of the patient's blood andis set by the potentiometer P4 which provides for precision regulation:

    (K C.sub.3 d/K C d) K'C = K'C.sub.3                        37.

equation 37 therefore provides an expression for the change with respectto time of the dilution curve that characterizes the dye concentrationand is unaffected by the change of oxygen saturation and by anydisturbance of the pulse curve. After a specific period of timefollowing the dye injection, the dye distributes in the blood and thefinal concentration value is formed, see also FIG. 2 - C_(3v). In viewof this, Equation 37 takes the following form:

    (K C.sub.3v d/K C d) K'C'= K' C.sub.3v                     38.

A signal proportional to the amount of blood in the blood circulation isdetermined by the quotient-forming circuit D (see FIG. 3) from theoutput signal K'C_(3v) of the quotient-forming and multiplier circuit MDand from the signal K"Qb which is set by the precision potentiometer P5and is proportional to the amount of dye injected into the blood of thepatient:

    (K"Qb/K'C.sub.3v) = K.sub.o (Qb/C.sub.3v) = K.sub.o V      39.

the signals which are proportional to the concentration values C₁, C₂,C₃ of the concentration sum C₁ + C₂ = C and are proportional to theoxygen saturation and the blood volume in the circulation can besuccessively displayed or recorded on the display unit DP or can be sodisplayed and recorded in parallel if several display units are used.

Another embodiment of the invention is illustrated in FIG. 4. Theoperation thereof is described by reference to Equations 7, 8 and 9.

If Equation 7 is multiplied with the multiplier circuit M7 by theconstant value α₁ /ε₁ and if the Equation 8 is subtracted therefrom bymeans of the subtraction circuit H6, the result will be: ##EQU11##

Only two unknown concentration values appear on the left-hand side ofthe equation or in the output signal of the subtraction circuit H6.

Equation 8 must be multiplied with the multiplier circuit M9 by theconstant value ε₃ /α₃ and Equation 7 must be subtracted therefrom bymeans of the subtraction circuit H5 to yield: ##EQU12##

Only two unknown concentration values occur on the right-hand side ofthe equation or in the output signal of the subtraction circuit H5.Equation 8 must be multiplied with the multiplier circuit M8 by aconstant value of β₃ /α₃ and Equation 9 subtracted therefrom by means ofthe subtraction circuit H7 to yield: ##EQU13##

Only two unknown concentration values are found on the right-hand sideof the equation or in the output signal of the subtraction circuit H7.

By analogy to FIG. 3, the remaining operations are performed by means ofthe multiplier circuits M10, M11 and M12, the subtracting circuits H5,H6, H7 and H8, the subtracting and scale setting circuits U3 and U4, thescale setting circuit G2 and the summing network Σ.

The signal which is proportional to C₂ is produced at the output of thescale setting circuit G2:

    y = k c.sub.2 d                                            30.

A signal which is proportional to C₃ is produced at the output of thesubtraction and scale setting circuit U3:

    w = k c.sub.3 d                                            34.

A signal which is proportional to C₁ appears at the output of thesubtraction and scale setting circuit U4.

U4:

    x = k c.sub.1 d                                            32.

A signal which is proportional to the sum C₁ + C₂ appears at the outputof the summing network Σ:

    X + Y = K C d                                              35.

An electrical signal which is independent of the thickness d of themeasured sample and is proportional only to the concentration C₃ isobtained from the output signals of the quotient-forming and multiplyingcircuit MD, the subtracting and scale setting circuit U₃ and the summingnetwork Σ and from the output signal K'C which is set by means of thepotentiometer P4 and is proportional to the known haemoglobin content ofthe patient.

    (K C.sub.3 d/K C d) K'C = K'C.sub.3                        37.

    (k c.sub.3v d/K C d) K'C = K'C.sub.3v                      38.

The value of K'C_(3v) can be displayed or the value K'C_(3v) set by theprecision potentiometer P6 together with the value K"Q_(b), set by theprecision potentiometer P5, can be connected to the quotient-forming andmultiplier circuit MD. The blood volume in the circulation is thusdetermined by forming the quotient from the two signals. ##EQU14##

The oxygen saturation of the blood is determined in like manner in thequotient-forming and multiplier circuit MD, namely from the outputsignal of the subtracting and scale setting circuit U4 from the outputsignal of the summing network Σ: ##EQU15##

The concentration values C1, C2, C3 and C as well as the values of S andV can be displayed and recorded successively on the same display unit orparallel to each other if several display units are provided.

Different embodiments of the invention will be explained by reference toFIGS. 5, 6, 7, 8, 9, 10, 11, 12, 13 and 14. The computing operationsexplained by reference to FIGS. 3 and 4 can be applied correspondinglyto these embodiments.

In the embodiment according to FIG. 5, the output of the channelamplifier A1 is connected directly to one input of a subtracting circuitH9, the output of the channel amplifier A2 being directly connected tothe input of the subtracting circuit H10 and H11. In like manner, thechannel amplifier A1 is connected through the multiplier circuit M13,the channel amplifier A2 is connected through the multiplier circuit M14and the channel amplifier A3 is connected through the multiplier circuitM15 to the other input of the subtraction circuits H11, H9 and H10respectively. The output signal of the subtraction circuits H9, H10 andH11 can be expressed through functions f(C₂,C₃), f(C₁,C₂) which containtwo unknown concentration values and can also be expressed by thefunction f(C₁,C₂).

According to FIG. 6 the output of the channel amplifier A1 is directlyconnected to one output of each of the subtraction circuits H12 and H13,but the channel amplifier A3 is directly connected to one input of thesubtraction circuit H14. The channel amplifier A1 is also connectedthrough the multiplier circuit M16 and the channel amplifier A2 isconnected through the multiplier circuit M17 and M18 to the other inputof the subtraction circuits H14, H13 and H12. The output signals of thesubtraction circuits H12, H13 and H14 are expressed in sequence by thefunctions f(C₁, C₃), f(C₁, C₂) and f(C₁, C₂).

According to FIG. 7, the output of the channel amplifier A1 is directlyconnected to one input of the subtraction circuit H17 and the output ofthe channel amplifier A2 is directly connected to one input of thesubtraction circuit H15 and H16.

Furthermore, the channel amplifiers A1 and A3 are connected via themultiplyier circuits M19 and M20 and the channel amplifier A3 isconnected through the multiplier circuit M21 to the other inputs of thesubtraction circuits H15, H16 and H17. The output signals of thesubtraction circuits H15, H16 and H17 can be expressed in sequence bythe functions f(C₂, C₃), f(C₁, C₂) and by f(C₁, C₂).

According to FIG. 8, the output of the channel amplifier A1 is connectedto one input of the subtraction circuit H18 and the output of thechannel amplifier A2 is directly connected to one input of thesubtraction circuit H19 and H20. The channel amplifier A1 is connectedon the one hand through the multiplier circuit M22 and the channelamplifier A3 through the multiplier circuits M23 and M24 to to the otherinput of the subtracting circuits H20, H19 and H18. The output signalsof the subtracting circuits can be expressed in sequence by thefunctions f(C₁, C₂) and f(C₁, C₂) or f(C₂, C₃).

According to FIG. 9, the output of the channel amplifier A2 is directlyconnected to one input of the subtracting circuit H21 and H22, theoutput of the channel amplifier A3 is directly connected to one input ofthe subtracting circuit H23 but the output of the channel amplifier A1is connected through the multiplier circuits M25, M26 and M27 to theother inputs of the subtracting circuits H23, H22 or H21.

The output signals of the subtracting circuits can be expressed insequence by the functions f(C₁, C₃), f(C₁, C₂) or f(C₁, C₂).

According to FIG. 10, the output of the channel amplifier A2 is directlyconnected on the one hand to one input of each of the subtractingcircuits H24, H25 and H26 and is connected on the other hand through themultiplier circuits M28 or M29 and the output of the channel amplifierA3 is connected through the multiplier circuit M30 to the other input ofthe subtracting circuit H26. the output signals of the subtractingcircuits H24, H25 and H26 can each be expressed in sequence by thefunctions f(C₂, C₃), f(C₁, C₂) or f(C₁, C₂).

The signals which correspond to the individual concentration values canbe produced in accordance with the embodiments illustrated in FIGS. 11,12, 13 and 14 from the output signals of the subtracting circuits whichfollow the channel amplifiers, said subtracting circuits representing alinear equation with two unknowns.

One input of subtracting circuit H27 and of the scale setting circuitand subtracting circuit U5 is directly connected to the output of thesubtracting circuit H3 according to FIG. 3. The output of thesubtracting circuit H1 is connected through the multiplying circuits M31and M32 to the input of the subtracting and scale setting circuit U2 andto the subtracting circuit H27. A signal proportional to C₁ appears atthe output of the subtracting and scale setting circuit U5 and a signalproportional to C₂ appears at the output of the subtracting circuit H27.The scale setting circuit G3 is provided for setting up the correctscale of the signal produced at the output of the subtracting circuitH27 and the summing network Σ (see FIGS. 3 and 11) is provided to formthe signal which is proportional to C. If an input of the subtractingcircuit H27 and of the subtracting and scale setting circuit U5 isdirectly connected to the output of the subtracting circuit H7 (FIG. 4)and if the output of the subtracting circuit H5 is connected through themultiplying circuits M31 and M32 to the other input of the subtractingand scale setting circuit U5 and to the subtracting circuit H27, asignal which is proportional to C₁ will be obtained from the output ofthe subtracting and scale setting circuit U5, but a signal which isproportional to C₂ will be obtained from the output of the subtractingcircuit H27. A scale setting circuit G3 is provided for correctadjustment of the output signal from the subtracting circuit H27 and thesumming network Σ (see FIGS. 4 and 11) one input of which is connectedto the output of the subtracting and scale setting circuit U5, isprovided to form the signal which is proportional to C. The output ofthe scale setting circuit G3 is connected to the other input of thesumming network Σ (see FIGS. 4 and 11).

One input of the subtracting circuit H27 and of the subtracting andscale setting circuit U5 is connected directly to the output of thesubtracting circuit H10 (FIG. 5). On the other hand, the output of thesubtracting circuit H11 is connected through the multiplier circuits M31and M32 to the other input of the subtracting circuits H27 andsubtracting and scale setting circuit U5. A signal which is proportionalto C₁ is produced at the output of the subtracting and scale settingcircuit U5 and a signal which is proportional to C₂ is produced at theoutput of the subtracting circuit H27, that means of the scale settingcircuit G3 (see FIGS. 5 and 11).

One input of the subtracting circuit H27 and of the subtracting andscale setting circuit U5 can be connected directly to the output of thesubtracting circuit H13, the output of the subtracting circuit H14 beingconnected through the multiplying circuits M31 and M32 to the otherinput of the subtracting and scale setting circuit U5 and of thesubtracting circuit H27. A signal which is proportional to C₂ isproduced at the output of the subtracting and scale setting circuit U5and a signal which is proportional to C₁ is produced at the output ofthe scale setting circuit G3 that means of the subtracting circuit H27(see FIGS. 6 and 11).

The output of the subtracting circuit H19 (according to FIG. 8) isconnected directly to one input of the subtracting circuit H27 or of thesubtracting and scale setting circuit U5 and the output of thesubtracting circuit H20 is connected through the multiplier circuits M31and M32 to the other input of the subtracting and scale setting circuitU5 and that of the subtracting circuit H27. A signal which isproportional to C₁ is thus produced at the output of the subtracting andscale setting circuit U5 and a signal which is proportional to C₂ isproduced at the output of the subtracting circuit H27 and of the scalesetting circuit G3 (see FIGS. 8 and 11).

The output of the subtracting circuit H22 (FIG. 9) can be connecteddirectly to one input of the subtracting circuit H27 and to thesubtracting and scale setting circuit U5 while the output of thesubtracting circuit H23 can be connected via the multiplying circuitsM31 and M32 to the other input of the subtracting and scale settingcircuit U5 and of the subtracting circuit H27. In this case, a signalwhich is proportional to C₁ is produced at the output of the subtractingand scale setting circuit U5 and a signal which is proportional to C₂ isproduced at the output of the subtracting circuit H27 and of the scalesetting circuit G3 (see FIGS. 9 and 11).

The output of the subtracting circuit H25 (according to FIG. 10) isconnected directly to one input of the subtracting circuit H27 and ofthe subtracting and scale setting circuit U5 and the output of thesubtracting circuit H26 is connected via the multiplying circuits M32and M31 to the other input of the subtracting circuit H27 or of thesubtracting and scale setting circuit U5. In this case, a signal whichis proportional to C₁ is produced at the output of the subtracting andscale setting circuit U5 and a signal which is proportional to C₂ isproduced at the output of the subtracting circuit H27 and of the scalesetting circuit G3 (see FIGS. 10 and 11).

The output of the subtracting circuit H10 (see FIG. 5) is connecteddirectly on the one hand to one input of the subtracting and scalesetting circuit U6 and on the other hand is connected through themultiplier circuit 33 to one input of the subtracting circuit H28. Theother input of the subtracting circuit H28 and of the subtracting andscale setting circuit U6 can be connected to the output of thesubtracting circuit H11. In this case, a signal which is proportional toC₁ will be produced at the output of the subtracting and scale settingcircuit U6 and a signal which is proportional to C₂ will be produced atthe output of the subtracting circuit H28 and of the scale settingcircuit G4. A summing network Σ (see FIGS. 5 and 12) one input of whichis connected to the output of the subtracting and scale setting circuitU6 while the other input is connected to the output of the scale settingcircuit G3 is provided to form a signal which is proportional to C.

The output of the subtracting circuit H13 according to FIG. 6 isdirectly connected on the one hand to one input of the subtracting andscale setting circuit U6 and on the other hand via the multipliercircuit M33 to the subtracting circuit H28, while the input thereof ofcan be connected to the output of the subtracting circuit H14 and on theother hand the input of the subtracting and scale setting circuit U6 canbe connected via the multiplier circuit M34. In this case, a signalwhich is proportional to C₂ will be produced at the output of thesubtracting and scale setting circuit U6 and a signal which isproportional to C₁ will be produced at the output of the subtractingcircuit H28 and of the scale setting circuit G4 (see FIGS. 6 and 12).

The output of the subtracting circuit H16 (according to FIG. 7) can bedirectly connected on the one hand to one input of the subtracting andscale setting circuit U6 and on the other hand one input of thesubtracting circuit H28 can be connected through the multiplier circuitM33 to the output of the subtracting circuit H17, but the other input ofthe subtracting circuit H28 can be connected on the other hand through amultiplier circuit M34 to the input of the subtracting and scale settingcircuit U6. In this case, a signal proportional to C₁ is produced at theoutput of the subtracting and scale setting circuit U6 and a signalproportional to C₂ is produced at the output of the subtracting circuitH28 and of the scale setting circuit G4 (see FIGS. 7 and 12).

The output of the subtracting circuit H18 (FIG. 8) is connected directlyto one input of the subtracting circuit H28, on the one hand through thesubtracting and scale setting circuit U6, and on the other hand throughthe multiplier circuit M23, but is connected to the other input of thesubtracting and scale setting circuit U6 partially through themultiplier circuit M34 and partially through the subtracting circuitH28. In this case, a signal proportional to C₁ is produced at the outputof the subtracting and scale setting circuit U6 and a signal which isproportional to C₂ is produced at the output of the subtracting circuitH28 and of the scale setting circuit G4 (see FIGS. 8 and 12).

The output of the subtracting circuit H22 according to FIG. 9 can beconnected directly to one input of the subtracting circuit H28, on theone hand through the subtracting and scale setting circuit U6 and on theother hand through the multiplier circuit M23, while the other input ofthe subtracting and scale setting circuit is connected to the output ofthe subtracting circuit H23, namely through the multiplier circuit M34and through the subtracting circuit H28. In this case, a signal which isproportional to C₁ will be produced at the output of the subtracting andscale setting circuit U6 and a signal which is proportional to C₂ willbe produced at the output of the subtracting circuit H28 and of thescale setting circuit G4 (see FIGS. 9 and 12).

The output of the subtracting circuit H25 according to FIG. 10 can beconnected directly to one input on the other hand of the subtracting andscale setting circuit U6 and on the other hand, through the multipliercircuit M33, to the subtracting circuit H28. The other input of thesubtracting circuit H28 on the one hand is connected to the output ofthe subtracting circuit H26 and on the other hand the other input of thesubtracting and scale setting circuit U6 is connected thereto throughthe multiplier circuit M34. In this case, a signal which is proportionalto C₁ is produced at the output of the subtracting and scale settingcircuit U6 and a signal which is proportional to C₂ is produced at theoutput of the subtracting circuit H28 and of the scale setting circuitG4 (see FIGS. 10 and 12).

The value of the remaining concentration is determined by the circuitsin accordance with FIGS. 13 and 14. The output of the subtractingcircuit H9 (FIG. 5) or H12 (FIG. 6) or H15 (FIG. 7) or H20 (FIG. 8) orH21 (FIG. 9) or H24 (FIG. 10) is connected directly to one input of thesubtracting and scale setting circuit U7. These subtracting circuits arealso directly connected to the channel amplifier. The output of thesubtracting circuit H27 (FIG. 11) or H28 (FIG. 12) is connected to theother input of the subtracting and scale setting circuit U7, thelast-mentioned output being connected through the multiplier circuitM35. In this case, a signal which is proportional to the concentrationC₃ will appear at the output of the subtracting and scale settingcircuit U7.

The output of the subtracting circuits H9 (FIG. 5) or H12 (FIG. 6) orH15 (FIG. 7) or H20 (FIG. 8) or H21 (FIG. 9) or H24 (FIG. 10) whichfollows the channel amplifiers is connected through the multipliercircuit M35 to one input of the subtracting and scale setting circuit U8while the other input thereof is directly connected to the output of thesubtracting circuit H27 (FIG. 11) or H28 (FIG. 12). In this case, asignal which is proportional to the concentration C₃ is produced at theoutput of the subtracting and scale setting circuit U8.

Other embodiments of the invention are illustrated in FIGS. 15 to 31.The operation of these embodiments is explained by reference to thecircuit according to FIG. 15 and based on Equations 7, 8 and 9.

If Equation 7 is multiplied with the multiplier circuit M37 by theconstant value α₁ /ε₁ and if the Equation 8 is subtracted therefrom bymeans of the subtracting circuit H30, the result will be: ##EQU16##

By using the designations introduced earlier the following relationshipis obtained:

    Z.sub.4 = K.sub.7 C.sub.3 d + K.sub.8 C.sub.3 d            44.

By multiplying Equation 8 with a multiplier circuit M39 by a constant avalue ε₃ /α₃ and by subtracting therefrom the Equation 7 by means of thesubtracting circuit H29, the following expression will be obtained:##EQU17##

The following relationship is obtained by using the terms which wereintroduced earlier:

    Z.sub.5 = K.sub.9 C.sub.1 d + K.sub.10 C.sub.2 d           46.

If Equation 8 is multiplied with the multiplying circuit M38 by aconstant value β₃ /α₃ and if Equation 9 is subtracted therefrom by meansof the subtracting circuit H32, the following relationship will beobtained: ##EQU18##

The following relationship will be obtained by using the terms whichwere introduced earlier:

    Z.sub.6 = K.sub.11 C.sub.1 d + K.sub.12 C.sub.2 d          48.

If Equation 9 is multiplied with the multiplying circuit M40 by aconstant value α₁ /β₁ and if Equation 8 is subtracted therefrom by meansof the subtracting circuit M31, the following relationship will beobtained: ##EQU19##

By introducing the simplifying term, the following relationship isobtained:

    Z.sub.7 = K.sub.13 C.sub.2 d + K.sub.14 C.sub.3 d          50.

Equations 44, 46, 48 or 50 which express the output signals of thesubtracting circuits H30, H29, H32 and H31 contain only two unknownconcentration values.

If Equation 44 is multiplied with the multiplying circuit M42 by aconstant value K₁₃ /K₇ and if Equation 50 is subtracted therefrom bymeans of the subtracting and scale setting circuit U10, the followingrelationship will be obtained: ##EQU20##

The term σ₃ ' is a factor for setting the scale. By using the termsintroduced earlier, the equation takes the following form:

    W = K C.sub.3 d                                            52.

A signal which is and proportional to the concentration C₃ willtherefore be produced at the output of the subtracting and scale settingcircuit U10.

If Equation 48 is multiplied with the multiplying circuit M43 by aconstant value K₉ /K₁₁ and if Equation 46 is subtracted therefrom withthe subtracting and scale setting circuit U11, the followingrelationship will be obtained: ##EQU21##

By using the terms introduced earlier, the equation will take thefollowing form:

    Y = K C.sub.3 d                                            54.

A signal which is proportional to the concentration C₂ is produced atthe output of the subtracting and scale setting circuit. If Equation 46is multiplied with the multiplying circuit M41 by a constant value K₁₂/K₁₀ and if Equation 48 is subtracted therefrom by means of thesubtracting and scale setting circuit U9, the following relationshipwill be obtained: ##EQU22##

The term σ₁ ' is a factor which refers to the scale setting. By usingthe terms introduced earlier, the following relationship will beobtained:

    X = K C.sub.1 d                                            56.

A signal which is proportional to the concentration C₁ is produced atthe output of the subtracting and scale setting circuit U9.

Equation 52, 54 and 55 are processed as already explained in accordancewith FIGS. 3 and 4. These operations also apply accordingly to theembodiments according to FIGS. 16-31.

According to FIG. 16, the output of the channel amplifier A1 is directlyconnected to one input of each of the subtracting circuits H33, H34, H35and H36, while the other input of the subtracting circuits H33 and H35is connected to the channel amplifier A2 via the multiplier circuits M45and M44 and the channel amplifier A3 is connected to the other input ofthe subtracting circuits H34 and H36 through the multiplier circuits M47and M46. The output signals of the subtracting circuits H33, H34, H35and H36 can be expressed in sequence by the functions f(C₁, C₃), f(C₁,C₂), f(C₂, C₃) and f(C₁, C₂).

The output of the channel amplifier A1 according to FIG. 17 is connecteddirectly to one input of the subtracting circuits H37 and H38 and theoutput of the channel amplifier A2 is directly connected to one input ofthe subtracting circuits H39 and H40. The output of the channelamplifier A3 is directly connected through the multiplier circuits M48,M49, M50 and M51 to the other input of the subtracting circuits H37,H38, H39 and H40. The output signals of the subtracting circuits H37,H38, H39 and H40 can be expressed by the corresponding functions f(C₁,C₂), f(C₁, C₂), f(C₂, C₃) and f(C₂, C₃).

According to FIG. 18, the amplifier output of the channel amplifier A1is connected directly to one input of the subtracting circuit H41 andthe amplifier output of the channel amplifier A2 is directly connectedto one output of each of the subtracting circuits H42, H43 and H44,while the output of the channel amplifier A1 is connected through themultiplier circuits M52 and M53 to the other input of the subtractingcircuits H43 and H42 and the output of the channel amplifier A3 isconnected through the multiplier circuits M54 and M55 to the other inputof the subtracting circuits H44 and H41. The output signals of thesubtracting circuits H41, H42, H43 and H44 can be expressed accordinglyby the functions f(C₁, C₂), f(C₁, C₂), f(C₂, C₃) and f(C₂, C₃).

The amplifier output of the channel amplifier A1 according to FIG. 19 isdirectly connected to one input of the subtracting circuits H45 and H46and the amplifier output of the channel amplifier A2 is directlyconnected to one input of the subtracting circuits H47 and H48.

The output of the channel amplifier A2 is also connected through themultiplier circuits M56 and M57 to the other input of the subtractingcircuit H46 and H45 and the output of the channel amplifier A3 isconnected through the multiplier circuits M58 and M59 to the other inputof the subtracting circuits H48 and H47. Depending on the sequence, theoutput signals of the subtracting circuits H45, H46, H47 and H48 can beexpressed by the functions f(C₁, C₂), f(C₂, C₃), f(C₁, C₂) and f(C₂,C₃).

The output of the channel amplifier A1 according to FIG. 20 is directlyconnected to one input of each of the subtracting circuits H49 and H50and the output of the channel amplifier A2 is directly connected to oneoutput of each of the subtracting circuits H51 and H52. The output ofthe channel amplifier A2 is connected through the multiplier circuit M60to the other input of the subtracting circuit H50 and the output of thechannel amplifier A3 is connected through the multiplier circuits M61,M62 and M63 to the other input of the subtracting circuits H51, H49 andH52.

Depending on the sequence, the output signals of the subtractingcircuits H49, H50, H51, H52 can be expressed by the functions f(C₁, C₂),f(C₂, C₃), f(C₁, C₂) and f(C₂, C₃).

In another embodiment according to FIG. 21, the output of the channelamplifier A1 is directly connected to one input of each of thesubtracting circuits H53 and H54 and the output of the channel amplifierA2 is directly connected to the one input of the subtracting circuitsH55 and H56. At the same time, the output of the channel amplifier A1 isconnected through the multiplier circuit M64 to the other input of thesubtracting circuit H55, the output of the channel amplifier A2 isconnected through the multiplier circuit M65 to the other input of thesubtracting circuits H54 while the output of the channel amplifier A# isconnected through the multiplier circuits M66 and M67 to the other inputof the subtracting circuits H56 and H53. Depending on the sequence, theoutput signals of the subtracting circuits H53, H54, H55, H56 can beexpressed by the functions f(C₁, C₂), f(C₁, C₂), f(C₂, C₃) and f(C₂,C₃).

In considering another embodiment according to FIG. 22 it will be seenthat the output of the channel amplifier A1 is connected directly to oneinput of the subtracting circuit H57, while the output of the channelamplifier A2 is directly connected to one output of each of thesubtracting circuits H58, H59 and H60. The output of the channelamplifier A1 is connected through the multiplier circuit M60 to theother input of the subtracting circuit H58, and the output of thechannel amplifier A3 is connected through the multiplier circuits M69,M70 and M71 to the other input of each of the subtracting circuits H59,H60 and H57. Depending on the sequence, the output signals of thesubtracting circuits H57, H58, H59 and H60 can be expressed by thefunctions f(C₁, C₂), f(C₂, C₃), f(C₁, C₂), f(C₂, C₃).

In another embodiment according to FIG. 23, the output of the channelamplifier A1 is connected directly to one input of the subtractingcircuit H61, but the output of the channel amplifier A2 is directlyconnected to one input of each of the subtracting circuits H62, H63 andH64, while on the other hand the output of the channel amplifier A1 isconnected through the multiplier circuit M72 to the other input of thesubtracting circuit H62 and the output of the channel amplifier A2 isconnected through the multiplier circuit M72 to the other input of thesubtracting circuit H61 and the output of the channel amplifier A3 isconnected through the multiplier circuits M74 and M75 to the other inputof each of the subtracting circuits H64 or H63. Depending on thesequence, the output signals of the subtracting circuits can thus beexpressed by the functions f(C₁, C₂), f(C₂, C₃), f(C₁, C₂) and f(C₂,C₃).

The embodiment according to FIG. 24 is as follows. The output of thechannel amplifier A1 is connected directly to one input of thesubtracting circuit H65, the output of the channel amplifier A2 isdirectly connected to one input of each of the subtracting circuits H66and H67 and the output of the channel amplifier A3 is directly connectedto one input of the subtracting circuit H68. At the same time, theoutput of the channel amplifier A1 is connected through the multipliercircuits M76 and M77 to the other input of each of the subtractingcircuits H66 and H68, the output of the channel amplifier A3 isconnected through the multiplier circuits M78 and M79 to the other inputof each of the subtracting circuits H67 and H65. Depending on thesequence, the output signals of the subtracting circuits can thus beexpressed by the functions f(C₁, C₂), f(C₁, C₂), f(C₂, C₃) and f(C₂,C₃).

In the embodiment according to FIG. 25, the output of the channelamplifier A1 is connected directly to one input of the subtractingcircuit H69, the output of the channel amplifier A2 is directlyconnected to one input of the subtracting circuit H70 and H71, and theoutput of the channel amplifier A3 is directly connected to one input ofthe subtracting circuit H72. At the same time, the output of the channelamplifier A1 is connected through the multiplier circuits M80, M81 andM82 to the other input of each of the subtracting citcuits H72, H71 andH70 and the output of the channel amplifier A3 is connected through themultiplier circuit M83 to the other input of the subtracting circuitH69. Depending on the sequence, the output signals of the subtractingcircuits H69, H70, H71 and H72 can thus be expressed by the functionsf(C₁, C₂), f(C₁, C₂), f(C₂, C₃) and f(C₂, C₃).

In another embodiment according to FIG. 26, the output of the channelamplifier A1 is connected directly to one input of the subtractingcircuit H73, the output of the channel amplifier A2 is directlyconnected to one input of each of the subtracting circuits H74 and H75,the output of the channel amplifier A3 however is directly connected toone input of the subtracting circuit H76.

At the same time, the output of the channel amplifier A1 is connectedthrough the multiplier circuits M84 and M85 to the other input of eachof the subtracting circuits H74 and H75, the output of the channelamplifier A2 is connected through the multiplier circuit M86 to theother input the subtracting circuit H76, the output of the channelamplifier A3 is connected through the multiplier circuit M87 to theother input of the subtracting circuit H73. Depending on the sequence,the output signals of the subtracting circuits H73 - H76 are thereforeexpressed by the functions f(C₁, C₂), f(C₁, C₂), f(C₂, C₃) and f(C₂,C₃).

In the embodiment according to FIG. 27, the output of the channelamplifier A1 is connected directly to one input of the subtractingcircuit H77, the output of the channel amplifier A2 is directlyconnected to one input of each of the subtracting circuits H78 and H79,the output of the channel amplifier A3 is directly connected to oneinput of the subtracting circuit H80. At the same time, the output ofthe channel amplifier A1 is connected through the multiplier circuitsM88 and M79 to each of the other inputs of the subtracting circuits H78and H79, the output of the channel amplifier A2 is connected through themultiplier circuit M90 to the other input of the subtracting circuit H80and the output of the channel amplifier A3 is connected through themultiplier circuit M91 to the other input of the subtracting circuitH77. Depending on the sequence, the output signals of the subtractingcircuits H77, H78, H79 and H80 can be expressed by the functions f(C₁,C₂), f(C₂, C₃), f(C₁, C₂) and f(C₂, C₃ ).

In the embodiment according to FIG. 28, the output of the channelamplifier A2 is connected directly to one input of the subtractingcircuits H81 and H82 and the output of the channel amplifier A3 isdirectly connected to one input of each of the subtracting circuits H83and H84. At the same time, the output of the channel amplifier A1 isconnected through the multiplier circuits M82 and M93 to the other inputof each of the subtracting circuits H82 and H81 and the output of thesubtracting circuit H81 is connected through the multiplier circuit M94and the output of the subtracting circuit H82 is connected through themultiplier circuit M95 to the other input of the subtracting circuitsH83 and H84. Depending on their sequence, the output signals of thesubtracting circuits H81, H82, H83 and H84 can be expressed by thefunctions f(C₁, C₃), f(C₂, C₃), f(C₂, C₃) and f(C₁, C₃).

Further processing of the signals on the outputs of the subtractingcircuits according to FIGS. 16-28 containing two unknown concentrationvalues and each of them representing a linear equation is performed bymeans of the circuits illustrated in FIGS. 29, 30 and 31.

If the output of the subtracting circuit H29 (FIG. 15) is connected viathe multiplier circuits M96 and M97 to one input of each of thesubtracting or scale setting circuits U13 and U12 and the output of thesubtracting circuit H32 is connected directly to the other input of thesubtracting and scale setting circuits U12 and U13, a signalproportional to the concentration C₁ will be produced at the output ofthe subtracting and scale setting circuits U12 and a signal proportionalto the concentration C₂ will be produced at the output of thesubtracting and scale setting circuit U13 (see FIGS. 15 and 29).

In like manner if one output of each of the subtracting circuits H33(FIG. 16) or H37 (FIG. 17) or H41 (FIG. 18) or H45 (FIG. 19) or H49(FIG. 20) or H53 (FIG. 21) or H57 (FIG. 22) or H61 (FIG. 23) or H65(FIG. 24) or H69 (FIG. 25) or H73 (FIG. 26) or H77 (FIG. 27) isconnected through the multiplier circuit M96 and M97 (FIG. 29) to oneinput of each of the subtracting and scale setting circuits U13 and U12and furthermore if one output of each of the subtracting circuits H36(FIG. 16) or H39 (FIG. 17) or H42 (FIG. 18) or H47 (FIG. 19) or H51(FIG. 20) or H54 (FIG. 21) or H59 (FIG. 22) or H63 (FIG. 23) or H66(FIG. 24) or H70 (FIG. 25) or H74 (FIG. 26) or H79 (FIG. 27) is directlyconnected to the other input of each of the subtracting and scalesetting circuits U12 and U13 a signal, proportional to the concentrationC₁ and the signal, proportional to the concentration C₂ will be producedat the output of the subtracting and scale setting circuits U12 and U13.

In accordance with the previous statements, the signals which areproportional to the concentration C₁ and C₂ can be determined in such away that the output of the subtracting circuit H33 (FIG. 16) or H37(FIG. 17) or H41 (FIG. 18) or H46 (FIG. 19) or H49 (FIG. 20) or H53(FIG. 21) or H57 (FIG. 22) or H61 (FIG. 23) or H65 (FIG. 24) or H69(FIG. 25) or H73 (FIG. 26) or H77 (FIG. 27) on the one hand are directlyconnected to one input of the subtracting and scale setting circuit U14and on the other hand are connected through the multiplier circuit M98to one input of the subtracting and scale setting circuit U15 andfurthermore, if the output of the subtracting circuit H36 (FIG. 16) orH39 (FIG. 17) or H42 (FIG. 18) or H47 (FIG. 19) or H51 (FIG. 20) or H54(FIG. 21) or H59 (FIG. 22) or H63 (FIG. 23) or H66 (FIG. 24) or H70(FIG. 25) or H74 (FIG. 26) or H79 (FIG. 27) on the one hand is directlyconnected to the other input of the subtracting and scale settingcircuit U15 and on the other hand is connected through the multipliercircuit M99 to the other input of the subtracting and scale settingcircuit U14. The signal which is proportional to the concentration C₁and the signal, proportional to the concentration C₂ will appear at theoutput of the subtracting and scale setting circuits U14 and U15 (seeFIG. 30).

The third concentration value C₃ is determined by the circuit inaccordance with FIG. 31:

The output of the subtracting circuit H34 (FIG. 16) or H38 (FIG. 17) orH43 (FIG. 18) or H46 (FIG. 19) or H50 (FIG. 20) or H55 (FIG. 21) or H58(FIG. 22) or H62 (FIG. 23) or H67 (FIG. 24) or H71 (FIG. 25) or H75(FIG. 26) or H78 (FIG. 27) is connected via the multiplier circuit M100to one input of the subtracting and scale setting circuit U16, theoutput of the subtracting circuit H35 (FIG. 16) or H40 (FIG. 17) or H44(FIG. 18) or H48 (FIG. 19) or H52 (FIG. 20) or H56 (FIG. 21) or H60(FIG. 22) or H64 (FIG. 23) or H68 (FIG. 24) or H72 (FIG. 25) or H76(FIG. 26) or H80 (FIG. 27) is directly connected to the other input ofthe subtracting and scale setting circuit U16. A signal which isproportional to the concentration C₃ will be produced in this case atthe output of the subtracting and scale setting circuit U16.

Signals produced at the output of the circuits 29, 30 and 31 illustratedin FIG. 28 are processed by analogy.

What we claim is:
 1. An apparatus for determining the concentration of adye in a biological liquid, such as blood, comprising an optical sensingsystem, a counting system, a feed and control system and an indicatingapparatus, said counting system having an input with three channels inaccordance with the number of channels of the optical system, each ofsaid channels of said counting system having a logarithmic circuit orthe three channels together having a logarithmic circuit operating intime multiplex operation, and having three amplifiers, and foursubtraction circuits connected to said channel amplifiers; threesubtraction and scale setting circuits, each having an input, theoutputs of said subtraction circuits being connected to the inputs ofsaid three subtraction and scale setting circuits; a summing circuit;quotient forming circuit means; any two of the outputs of the lastmentioned subtraction and scale setting circuits being connected to theinput of said summing circuit, and the output of said summing circuitbeing connected to said indicating apparatus and to the input of saidquotient forming circuit means; the outputs of said subtraction andscale setting circuits being connected to the quotient forming circuitmeans; the outputs of the quotient forming circuit means being connectedto said indicating apparatus; and a fine adjustment potentiometerconnected to further inputs of said quotient forming circuit means. 2.An apparatus according to claim 1, wherein said subtraction circuits areconnected to said channel amplifiers via one multiplication circuiteach, and to the inputs of said three subtraction and scale settingcircuits via one multiplication circuit each.
 3. An apparatus accordingto claim 1, wherein said quotient forming circuit means is a quotientforming circuit.
 4. An apparatus according to claim 1, wherein saidquotient forming circuit means is a quotient forming and multiplyingcircuit, and wherein at least one fine adjustment potentiometer isconnected to the further inputs of said quotient forming and multiplyingcircuit.
 5. An apparatus for determining the concentration of a dye in abiological liquid, such as blood, comprising an optical sensing system,a counting system, a feed and control system and an indicatingapparatus, said counting system having an input with three channels inaccordance with the number of channels of the optical system, each ofsaid channels of said counting system having a logarithmic circuit orthe three channels together having a logarithmic circuit operating intime multiplex operation, and having three amplifiers, and threesubtraction circuits connected to said channel amplifiers, a pluralityof subtraction and scale setting circuits; the outputs of said threesubtraction circuits following the channel amplifiers being connected tosaid subtraction and scale setting circuits and to the input of a singlesubtraction circuit, the output of the last-mentioned single subtractioncircuit being connected to the input of one of said subtraction andscale setting circuits; a summing circuit; quotient forming circuitmeans; the output of said last-mentioned subtraction circuit beingfurthermore connected to the input of one of said scale setting circuitsand the output of said last-mentioned scale setting circuit as well asone of the outputs of said subtraction and scale setting circuits or theoutputs of said two last-mentioned subtraction and scale settingcircuits being connected to the input of said summing circuit; theoutput of said summing circuit being connected to the input of saidquotient forming circuit means and to the input of said indicatingdevice; the outputs of said scale setting circuit as well as the outputsof said subtraction and scale setting circuits being connected to theindicating device and to the input of the quotient forming circuitmeans; the outputs of the quotient forming circuit means being connectedto said indicating device; and a fine adjustment potentiometer connectedto further inputs of said quotient forming circuit means.
 6. Anapparatus according to claim 5, wherein said subtraction circuits areconnected to said channel amplifiers via one multiplication circuiteach, and to the inputs of said three subtraction and scale settingcircuits via one multiplication circuit each.
 7. An apparatus accordingto claim 5, wherein said quotient forming circuit means is a quotientforming circuit.
 8. An apparatus according to claim 5, wherein saidquotient forming circuit means is a quotient forming and multiplyingcircuit, and wherein at least one fine adjustment potentiometer isconnected to the further inputs of said quotient forming and multiplyingcircuit.